Mathematics

Integrate the following function with respect to $$x$$
$$\dfrac{(\sin^{-1}{x})^{3/2}}{\sqrt{1-x^{2}}}$$


SOLUTION
According to question,

Let,   $$sin^{-1}x=t$$

$$\implies \dfrac{1}{\sqrt{1-x^2}}dx=dt$$       

Substituting these values, we get

$$\implies \int t^{\frac{3}{2}}dt$$

$$\implies \dfrac{2t^{\frac{5}{2}}}{5}+C$$

$$\implies \dfrac{2(sin^{-1}x)^{\frac{5}{2}}}{5}+C$$

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Subjective Medium Published on 17th 09, 2020
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